photonics

: The phenomenon of the formation of microheterogeneities (MHs) in solutions, which, according to chemical handbooks, are considered true solutions, has been known for a long time. MHs have been found in more than 100 binary solutions, many of which are used both in various scientiﬁc studies and in life. However, the nature of this phenomenon is largely unclear. It is only well-known that MHs are stable areas of increased concentration of one of the components of the solution. The main reason for the poor knowledge of MHs is the use of very few experimental methods, mainly light scattering methods. In this paper, the terahertz time-domain spectroscopy method was used for the ﬁrst time to study MHs using the example of aqueous solutions of three sugars: glucose, fructose, and sucrose. This method gives the spectra of complex permittivity in the terahertz range, which are very informative when studying the hydrate shells of molecules in solutions. The idea of this study was that structuring sugar molecules with the formation of MHs changes their hydration. The characteristics of sugar hydration in solutions before and after ﬁltration through a 20 nm ﬁlter, leading to the destruction of MHs, were compared. It has been shown that the water binding in the MHs of all three solutions is increased compared with the hydrate shells of individual sugar molecules. Also, for MHs’ fructose solution, a decrease in the number of hydrogen bonds between water molecules and an increase in the number of free water molecules was shown, which is not observed in MH glucose and sucrose solutions. This is explained by mutarotations of fructose molecules, leading to permanent signiﬁcant rearrangements of the water structure in MHs. Thus, terahertz time-domain spectroscopy provides fundamentally new information about the MHs of aqueous solutions at the level of their hydration characteristics. The presence of MHs in solutions is a signiﬁcant factor that has never been taken into account when studying the hydrate shells of various molecules in solutions using THz spectroscopy.


Introduction
The phenomenon of the formation of microheterogeneities (MHs) in various solutions, which according to chemical handbooks, are considered true solutions, has a long history.For the first time, this was encountered by Vuks and Shurupova in 1972 [1], who discovered abnormal light scattering in the water-tertial butyl alcohol system, although they did not understand what this was due to.After that, the study of this phenomenon was repeatedly returned at a more advanced experimental level with the consideration of an increasing number of solutions, and these studies continue to this day.The most famous works were those of Sedlak [2][3][4], in which MHs (the author called them large-scale supramolecular structures) of more than 100 binary solutions were studied.
The MHs sizes for different solutions and conditions range from tens to hundreds of nm.In most cases, MHs are formed almost immediately after the preparation of the solution, although there are examples when their formation begins only after a day, for 2 of 13 example, in the case of a water/glycerol mixture [3].After formation, MHs remain stable for months [5] and even more than a year [3].During this time, extremely slow changes of MHs in concentration [2] or size distributions [3] are observed.The sizes and concentration of MHs can also vary with temperature, up to complete disappearance upon heating and re-formation upon cooling [6,7].
MHs are formed most efficiently in solutions containing dipolar protic molecules, which are capable of forming a spatial network of hydrogen bonds [4].All these criteria are best met by water, and it is quite natural that aqueous solutions have been studied more than others.
In many works, the filtration procedure (through 20-200 nm filters) of solutions was carried out, which, as a rule, eliminated MHs [6,8,9].In some cases, their formation was registered again [10,11], and in some, not [5].Some studies have shown that the chemical composition of solutions does not change after filtration [6,12].This means that filtering destroys the MHs, and does not filter them.
Despite more than half a century of MH research, their nature is unclear.Different versions were expressed.For example, MHs are associated with structural "phase transitions" [1], clathrate hydrate precursors [13], microphase separation [14], or even gas bubbles [15,16], and banal impurities [17].Today, it is clear that MHs are areas of a solution with an increased content of one of the components, behaving like discrete particles.At the same time, the key question remains about the mechanisms of long-term preservation of areas of increased concentration of a certain type of molecules in liquid solutions.
The main interest in this context is represented by aqueous solutions of various organics since they are related to most natural systems, including biological ones.The most reasonable interpretations of MHs to date have been expressed specifically for aqueous solutions of low-molecular-weight organics.According to one of them, MHs are formed as a result of the attraction of solute molecules to each other through hydrogen bond bridges from water molecules [4].In our previous works [7,[18][19][20], the formation of MHs in binary solutions was explained by a specific spinodal decomposition, which occurs under the influence of the dichotomous noise of twinkling hydrogen bonds between molecules of organic compound and water.
According to some authors, the presence of hydrophobic components is necessary for the formation of MHs in aqueous solutions [5,8,21].This makes it possible to form a hydrophobic-enriched core, around which a shell enriched with organic molecules is formed [22].It has been suggested that the formation of this kind of emulsion occurs under the influence of a hydrophobe, which helps to stabilize the concentration fluctuations of organic molecules in solution [21].According to another version, the MHs do not contain a single hydrophobic core and shell but consist of micelles of the described type with dimensions of the order of 10 nm, which combine into hydrogen-bound clusters of submicron sizes [23].
It is worth noting that the presence of hydrophobic impurities would be wrong to consider as the basis of MHs, which would be a typical artifact.Hydrophobes only serve as some kind of "seeds" for the formation of MHs.This is confirmed by the fact that only at optimal concentrations of organic substances (containing trace amounts of hydrophobic impurities) MHs are formed in aqueous solutions [6,7].With an increase in their concentrations, the amount of MH decreases until it completely disappears, although the content of the hydrophobic component increases.Hydrophobic impurities can be sufficient at the level of 0.005% [5] for the formation of MHs, occupying a significantly larger volume fraction of the solution.In such quantities, hydrophobes are contained in almost all reagents, even 99.9%purity, and appear when using plastic labware or when solutions are saturated with air.Natural hydrophobic components are also present in any biological system.Therefore, the study of MHs, even if they depend on trace hydrophobic impurities, is of both fundamental and applied interest.Among the applied aspects, methods of optimizing chemical reactions [24][25][26] and the possible use of MHs as drug carriers [23] were mentioned in the literature.
The lack of a full understanding of the structure of MHs is explained by the small number of experimental methods used to study these molecular formations.The basis of almost all works in this direction are methods of dynamic light scattering and multi-angle static light scattering [2,3,6,22].In isolated cases, cryomicroscopy [10], compressibility measurement [15], and polarimetry [27] were used in addition.The methods of small-angle neutron scattering [21], small-angle X-ray scattering [8], and osmometry [2] have also been used, but they are actually not sensitive to these low-contrast and weakly associated MHs.
These light scattering methods are sensitive to local changes in the concentration of molecules of one component of the solution, and the second component acts as an optically inert matrix.However, we can look at this phenomenon differently.If the molecules of one component are somehow structured relative to each other, this can contribute to a change in the state of the matrix due to solvophobic effects.If, for example, in aqueous solutions, solute molecules are grouped in MHs, this can lead to a change in their hydration.In other words, the state of the water inside MHs is different from the state of the water outside.
THz spectroscopy is one of the efficient and sensitive tools that can successfully probe the hydration shell of molecules [28][29][30][31][32].It is sensitive not only to the primary strongly bound hydrate shell but also to more distant areas of hydration with altered dynamics of water molecules [33][34][35].In our previous work, we analyzed solutions of proteins [36], phospholipids [35], nucleic acids [37,38], and sugars [39] using the THz time-domain spectroscopy (THz-TDS) method, which confirms the great possibilities of this method in the study of hydration.Also, in a recent work [40] on the study of aqueous solutions of alcohols by THz spectroscopy, it was shown that this method is very informative in the analysis of intermolecular hydrogen bonds and molecular micro-inhomogeneities.Only micro-heterogeneities were understood as the formation of self-aggregated directly bonded molecular structures, and not areas with a slightly increased concentration of a substance dissolved in water.However, judging by the literature data, THz spectroscopy has not previously been used to study MHs.
In this work, the THz-TDS method was used to study aqueous solutions of two monosaccharides, glucose and fructose, and a disaccharide based on them, sucrose.These solutions were analyzed before and after filtration, which leads to the destruction of MHs and the production of a molecular solution (without MHs).Differences in some parameters of hydration of solutions with MHs from solutions without MHs were found, which indicate a special type of hydration inside MHs.Significant differences in the hydration of MHs in solutions of different sugars were also found, which indicates that the structure of MHs depends on the type of molecules forming them.
Each solution was analyzed (as described in Sections 2.2-2.5)before and after filtration through a filter with a pore diameter of 20 nm (Anotop 10 0.02 µm, Whatman GmbH, Dassel, Germany).

Recording of Spectra Using THz-TDS Method
The spectra were recorded using a TPS Spectra 3000 spectrometer (Teraview, Cambridge, UK).The THz-TDS method records the time profile of the electric field strength E(t) of periodically generated picosecond electromagnetic pulses.After the complex Fourier transform of E(t), single-beam spectra of intensity and delay times of the pulse radiation are calculated.By recording these spectra for the sample and background, the absorption Tr(v) and the refractive index n(v) spectra of the sample are calculated.From these two spectra, complex dielectric spectra (DS) can be unambiguously calculated without using the Kramers-Kronig relations: where ε and ε are the real and imaginary parts of DS, ν is wavenumber, and l is sample thickness.The details of the THz-TDS method are well known and described in the literature [41].
The spectra were recorded in the range of 10-110 cm −1 (0.3-3.3 THz) with a resolution of 4 cm −1 .Averaging over 1200 E(t) functions was carried out for each spectrum.The Fourier transform was performed with the 3-term Blackmann-Harris apodization function using standard Teraview software.From the moment the sample was placed in the sample compartment to the beginning of the measurement, a pause of 5 min was made to stabilize the sample temperature and purge the spectrometer with dried air using FT-IR Purge Gas Generator 74-5041 (Parker Hannifin Corporation, Haverhill, MA, USA).The spectra of solutions were recorded in liquid cuvettes with z-cut quartz windows and placed in a thermostatic holder at a temperature of 25 ± 0.2 • C.
We aimed to achieve the highest quality of the spectra, so we did not use the common approach of recording the spectrum of a sample in a cuvette and the background spectrum of an empty cuvette.This approach leads to the presence of artifacts in the spectra due to differences in reflections from the surfaces of empty and filled cuvettes, etc. [42].Instead, the spectra of each solution were recorded in two identical cuvettes differing in the distance between the windows (sample thickness).The spectrum of the solution in a larger cell was recorded, and the spectrum of the same solution, but in a smaller cell, was used as the background spectrum.This allowed us to determine the spectra of the solution with a thickness equal to the difference in the thicknesses of the two cuvettes, and at the same time, avoid the artifacts mentioned above.The method of recording spectra is described in more detail in our earlier article [36].
The exact thicknesses of the sample in two cuvettes were determined based on the measurement of the distances between the windows of empty cuvettes using the interferometric method [43].The actual thicknesses were 50.06 and 100.26 µm; as a result, the spectra of solutions with a thickness of 50.2 µm were measured.
For each sample, 30 spectra were recorded for subsequent averaging and statistical analysis.

Subtracting the Contribution of Sugars from DS of Their Solutions
In this work, the task was to analyze the structural-dynamic characteristics of water in solutions using their DS.To accomplish this, it is necessary to subtract the contribution of dissolved sugars from solutions DS.Permittivity is a concept of the theory of electrodynamics of continuous media.From the point of view of this theory, sugar solution is two-phase system: one continuous aqueous phase with small inclusions of sugar molecules (second phase).The separation of the dielectric contributions of the phases is usually carried out using effective medium models [44].In this case, the Bruggeman model is quite suitable [45]: where f is the volume fraction of sugar in the solution; and ε * s , ε * w , and ε * i are dielectric permittivities of the sugar solution, the aqueous phase of the solution, and sugar molecules, respectively.In this case, all three permittivities are complex functions of frequency, i.e., DS.We used a similar approach to separating the dielectric contributions of phases for sugar solutions earlier [39].
The function ε * s was determined by direct measurement (see Section 2.2).The function ε * i was determined from the spectra of sugars in dry form (see Section 2.4).The value of f was calculated by multiplying the molar fraction of sugar in solution (0.5 mol%) by the molarity of solution in 1 cm 3 (0.055 mol) and by the specific volume of sugar molecules in solution (111.7 cm 3 /mol for glucose and fructose, 211.6 cm 3 /mol for sucrose) [46].This corresponds to about 3 vol% glucose and fructose, 5.8 vol% sucrose.
The solution of Equation ( 2) in the complex plane [36] allows us to find the real ε w and imaginary ε w parts of ε * w .

Preparation of Sugar Films and Determination of Their DS
As follows from Equation (2), to determine the DS of the aqueous phase ε * w of the solution, it is necessary to know the DS of sugars in dry form ε * i .Sugars samples for spectral measurements were prepared as follows.A total of 30 mg of sugar was poured between two 5 µm Teflon films.The lower film was placed on a smooth wooden surface, and a metal flat heater was applied to the upper film and heated to a temperature 3-5 • C above the melting point of sugar (which is lower than the melting point of Teflon).After melting the sugar, the heater was quickly replaced with a metal plate cooled in liquid nitrogen.Due to the sufficiently high glass transition temperature of sugar [47] and its thin layer, rapid cooling was realized, and an amorphous sugar film was formed.Obtaining an amorphous phase, and not a crystalline one, is necessary for the correct subtraction of the dielectric contribution of sugar from the DS solution.The fact is that sugar molecules are arranged randomly in the solution, as in the amorphous phase.In the case of crystalline sugar, its DS contains phonon bands, which are not present in chaotically arranged molecules in solution, and the use of such DS in the ratio (2) would be incorrect.The details of the description of the procedure for the preparation of amorphous sugars films were described by us earlier [39].
The transmission and refraction spectra of sugars films were recorded using a TPS Spectra 3000 spectrometer, and DS were calculated using Formula (1).The film thicknesses l were measured with a micrometer.

Analysis of the DS of Aqueous Phase of Solutions
The obtained DS of the aqueous phase of solutions were analyzed according to the following model: where τ 1 and ∆ε 1 are the time and strength of Debye's relaxation of water [48,49], τ 2 and ∆ε 2 are the time and strength of relaxation process related to free or weakly bound water molecules [50][51][52][53], A and ω 0 are the amplitude and the resonance frequency of intermolecular stretch vibrations of water molecules bound by hydrogen bonds, γ is a parameter standing for the width of this vibrational band [54,55], ε ∞ is high-frequency permittivity (a parameter that takes into account the dielectric response of all higherfrequency polarization processes of water), i is the imaginary unit, and ω is the cyclic frequency.Model (3) takes into account all the main types of molecular dynamics of water manifested in the THz range.This model is generally accepted today [38,51,[56][57][58].
Model DS (3) contains 8 parameters that can be calculated by fitting model DS to experimental ones.To reduce the uncertainty of the fitting, the number of variable parameters (3) has been reduced.The parameter ε ∞ was equated to 2.5; this is a characteristic value for dilute aqueous solutions at frequencies greater than ω 0 .
The maximum of the Debye band of aqueous solutions (the first term of Equation ( 3)) is strongly shifted to the low-frequency region (about 0.6 cm −1 [59]) relative to the analyzed frequency range, so we register only the high-frequency edge of this band.As is known [60][61][62], the Debye band is sensitive to hydration processes, and when binding water molecules in hydrate shells, it decreases in amplitude ∆ε 1 and shifts towards lower frequencies; that is, τ 1 increases.In the THz region under consideration, both the decrease in amplitude and the shift of the band maximum are displayed as a decrease in absorption at the low-frequency edge.In this regard, there is no need to consider both parameters independently, τ 1 and ∆ε 1 .The parameter τ 1 was equated to the value of 8.28 ps, typical for pure water at 25 • C [59].As a result, 6 independent parameters remained in model (3): ∆ε 1 , ∆ε 2 , τ 2 , A, ω 0 , and γ, which were calculated using a fitting.
Fitting was implemented by minimizing the value of s: where «mod» and «exp» are the model and experimental DS, and M = 250 is the number of points in the DS.Fitting was carried out for each experimental DS separately.The value s did not exceed 0.002, which indicates the high accuracy of calculations.Each of the calculated parameters describes a certain characteristic of the intermolecular structure and dynamics of water in the solution according to the meaning of the corresponding spectral band.The parameters of the Debye band reflect the connectivity of water molecules, the parameters of high-frequency relaxation characterize the dynamics of the fraction of free water molecules, and the parameters of the vibrational band contain information about intermolecular hydrogen bonding.Also, these parameters can be used to calculate the proportion of free water molecules in a solution using the equation obtained in our previous work [63]: where ε 0 is the electric constant, k is the Boltzmann constant, T is the absolute temperature, N is the number of water molecules per unit volume, and d is the electric dipole moment of a water molecule.

Measurement of Size Distributions of Optical Inhomogeneities in Solutions
The size (hydrodynamic diameter) distributions of optical inhomogeneities in sugar solutions were measured by dynamic light scattering on the Zetasizer Nano ZS (Malvern Instruments Ltd., Worcestershire, UK).Acrylic cuvettes were used (REF 67.740 Sarstedt, Nümbrecht, Germany).The accumulation of the correlation function in each individual measurement was 10 cycles of 15 s.The calculation of size distributions from correlation functions was performed using Malvern Instruments software.To accurately determine the sizes, reference values of viscosity and refractive index (at a measured temperature of 25 • C) of sugar solutions were set.Each sample was measured at least 6 times for the possibility of averaging.

Results
Figure 1 shows the size distributions of optical inhomogeneities in the studied solutions before and after filtration.Two size fractions are clearly visible in the initial solutions-one less than 1 nm, and the other about 200 nm.Small differences between solutions are not statistically significant.Obviously, the low-size peak in the distributions in Figure 1 refers to individual sugar molecules with some hydrate shell [2,64].A peak of about 200 nm reflects the presence of MHs in the studied solutions.As follows from Figure 1, after filtration, MHs disappear, and a molecular solution is obtained.
Figure 2 shows the transmission and refractive index spectra of the studied solutions.For clarity, solutions before filtration are called solutions containing MHs, and solutions after filtration are called molecular solutions.Figure 3a-c show the average DS of the aqueous phase of all studied solutions.For a visual representation of the DS differences between molecular solutions and solutions containing MHs, the difference spectra are presented in Figure 3d-f.Table 1 contains the values of the model parameters (3) calculated from the DS of the studied solutions.Figure 2 shows the transmission and refractive index spectra of the studied solutions.For clarity, solutions before filtration are called solutions containing MHs, and solutions after filtration are called molecular solutions.Figure 3a-c show the average DS of the aqueous phase of all studied solutions.For a visual representation of the DS differences between molecular solutions and solutions containing MHs, the difference spectra are presented in Figure 3d-f.Table 1 contains the values of the model parameters (3) calculated from the DS of the studied solutions.Figure 2 shows the transmission and refractive index spectra of the studied solutions.For clarity, solutions before filtration are called solutions containing MHs, and solutions after filtration are called molecular solutions.Figure 3a-c show the average DS of the aqueous phase of all studied solutions.For a visual representation of the DS differences between molecular solutions and solutions containing MHs, the difference spectra are presented in Figure 3d-f.Table 1 contains the values of the model parameters (3) calculated from the DS of the studied solutions.The difference spectra shown in Figure 3d-f indicate that with a decrease in frequency, starting from about 40 cm −1 , the molecular solution exhibits a stronger increase in dielectric losses (ε ) than the solution containing MHs.This is most pronounced for fructose solutions, in which the difference in ε at 10 cm −1 is 0.15, which is 2.5 times more than glucose solutions and 5 times more than sucrose solutions.Since the only spectral band of water located on the low-frequency side of the frequency range under consideration is the Debye band (the first term of Equation ( 3)), the increase in ε with a decrease in frequency indicates a greater amplitude of the Debye band ∆ε 1 for molecular solutions than for solutions containing MHs.This result is quantitatively displayed in Table 1.Table 1 also shows that the greatest difference in this parameter is observed between fructose solutions.Table 1.Parameters of the model DS (3) of the aqueous phase of solutions of 0.5 mol% glucose-, fructose-, and sucrose-containing MHs, and molecular solutions of the same composition (after filtration).n is the percentage of free water molecules calculated based on Equation (5).The shown dispersions are presented as 95% mean confidence interval for a sample of 30 values.Bold font indicates pairs of values that differ statistically significantly between the solution with MHs and the molecular solution.

Sugar solution
The difference spectra shown in Figure 3d-f indicate that with a decrease in frequency, starting from about 40 cm −1 , the molecular solution exhibits a stronger increase in Table 1.Parameters of the model DS (3) of the aqueous phase of solutions of 0.5 mol% glucose-, fructose-, and sucrose-containing MHs, and molecular solutions of the same composition (after filtration).n is the percentage of free water molecules calculated based on Equation (5).The shown dispersions are presented as 95% mean confidence interval for a sample of 30 values.Bold font indicates pairs of values that differ statistically significantly between the solution with MHs and the molecular solution.

Sugar
Also, in Figure 3e, it can be seen that there is a noticeable stable excess of the ε molecular solution of fructose compared with the solution containing MHs.This is due to the presence of greater absorption from higher frequencies (according to the Kramers-Kronig ratio); that is, the contribution of the band of intermolecular vibrations of water molecules (the third term of Equation ( 3)).This is also quantified in Table 1.

Discussion
As follows from Figure 1, after the filtration of sugar solutions, MHs disappear.Similar results have been repeatedly obtained for various aqueous solutions of organic matter [2,4,6].The disappearance of MHs is explained by the destruction of MHs, and not by their filtration in the exact sense.For some solutions, this was confirmed by the preservation of the chemical composition after filtration [6,12].This is natural; otherwise, the filter would be a large-cell membrane creating a concentration gradient, which is obviously impossible.
However, the destruction of MHs changes not only the distribution of sugar molecules in the solution, making it uniform, but also affects the structural-dynamic characteristics of the water in the solution.This follows from the differences in the DS of the aqueous phase of solutions containing and not containing MHs (Figure 3), although these differences are not so big.It is known that the spectra of aqueous solutions in the THz region are always uncharacteristic and visually not very informative.In this case, we can only see on a qualitative level that the greatest differences in DS are observed between fructose solutions (with and without MHs).However, the main results that can be clearly interpreted are reflected in the parameter values calculated from DS (Table 1).
It follows from Table 1 that for solutions of all three sugars, the presence of MHs leads to a decrease in the strength of the Debye relaxation ∆ε 1 .In the theory of dielectric spectroscopy, a decrease in ∆ε 1 indicates an increase in the binding of water molecules [60][61][62].That is, there is a stronger binding of water molecules inside MHs than outside MHs (in a molecular solution).
The MHs of fructose solution exhibit the strongest binding of water molecules and, in addition, demonstrate an increase in the number of free water molecules n and a decrease in the parameter A/ω 2 0 .The last parameter describes the contribution of intermolecular vibrations of water molecules bound by hydrogen bonds to the overall dielectric response [38,39,43].According to the meaning of this vibrational band, a decrease in its amplitude can be the result of two reasons: a decrease in the number of hydrogen bonds (the number of molecular oscillators) or a decrease in the average dipole moment of intermolecular oscillations.A decrease in the dipole moment of the oscillation is associated with a decrease in the amplitude of the oscillation, which, as is known, is associated with an increase in the bond energy [65].Since the average energy of hydrogen bonds is directly related to the resonant frequency ω 0 , which does not differ between solutions (Table 1), the decrease in the parameter A/ω 2 0 is explained by a decrease in the number of hydrogen bonds.Thus, in the MHs of the fructose solution, in addition to strengthening the binding of water, a decrease in the number of hydrogen bonds and an increase in the number of free water molecules were registered.That is, the structure of water inside the MHs of fructose solution is not homogeneous and contains both areas of increased water connectivity and areas of destroyed structure.
It is important to note that, judging by the parameters of Table 1, no manifestations of the destroyed structure of water in MHs of glucose and sucrose solutions were detected.This indicates the differences in MHs structures formed on the basis of different sugars.The main difference between fructose and glucose or sucrose is the great variability of its structure.At room temperature, the following forms of fructose molecules are present in an aqueous solution [66]: β-fructopyranose (71.4%), β-fructofuranose (22.3%), α-fructofuranose (5.5%), and keto-fructose and α-fructopyranose, which are in dynamic equilibrium, constantly transforming into each other.Sucrose does not contain anomeric carbon atoms.Glucose has transitions between α-(35%) and β-form (65%) [67], but these are very similar anomers in structure, differing only in the orientation of the 1-OH group.That is, only fructose has significant rearrangements between furanose and pyranose forms, which, apparently, serves as a permanent factor in the destabilization of the water structure inside MHs, leads to the destruction of part of the hydrogen bonds and, as a consequence, to the release of more free water molecules.
It is known that the extent of sugar hydration, which can be detected by THz spectroscopy, is about 0.5 nm from the surface of the molecule [55, 68,69].For the sugar concentrations used, the average distance between the centers of mass of sugar molecules in solution is about 1.8 nm with a uniform distribution by volume.If we take into account the size of the sugar molecules, about 0.5 nm, then the average distance between them in a molecular solution is comparable to the thickness of hydrate shells.The distance between sugar molecules in MHs should be less.Hydrate shells inside MHs overlap significantly, which leads to significant differences in hydration inside MHs and individual sugar molecules.This is exactly what we see by the difference in the parameters (Table 1) of solutions containing MHs from molecular solutions of identical chemical composition.
It is important to note that in the works where the characteristics of sugar hydration were evaluated based on the analysis of their THz spectra [39,52,55,68,69], the presence of MHs was not considered at all.It is obvious that taking into account the presence of MHs in solutions can noticeably correct the conclusions made earlier.Figure 4 compares the main parameters of hydration in the studied solutions with the parameters of pure water.
only fructose has significant rearrangements between furanose and pyranose forms, which, apparently, serves as a permanent factor in the destabilization of the water structure inside MHs, leads to the destruction of part of the hydrogen bonds and, as a consequence, to the release of more free water molecules.
It is known that the extent of sugar hydration, which can be detected by THz spectroscopy, is about 0.5 nm from the surface of the molecule [55, 68,69].For the sugar concentrations used, the average distance between the centers of mass of sugar molecules in solution is about 1.8 nm with a uniform distribution by volume.If we take into account the size of the sugar molecules, about 0.5 nm, then the average distance between them in a molecular solution is comparable to the thickness of hydrate shells.The distance between sugar molecules in MHs should be less.Hydrate shells inside MHs overlap significantly, which leads to significant differences in hydration inside MHs and individual sugar molecules.This is exactly what we see by the difference in the parameters (Table 1) of solutions containing MHs from molecular solutions of identical chemical composition.
It is important to note that in the works where the characteristics of sugar hydration were evaluated based on the analysis of their THz spectra [39,52,55,68,69], the presence of MHs was not considered at all.It is obvious that taking into account the presence of MHs in solutions can noticeably correct the conclusions made earlier.5).Data for water are taken from our previous work [39].
As follows from Figure 4a, the hydration of individual sugar molecules in solution is accompanied by much less strengthening of water binding than hydration of MHs.The increase in the number of free water molecules due to the hydration of individual fructose molecules is less than due to the hydration of MHs (Figure 4b).At the same time, the hydration of individual fructose molecules is accompanied by a greater increase in the number of hydrogen bonds than with MHs hydration (Figure 4c).Thus, the previously obtained data in various papers on the characteristics of the hydration of sugar molecules based on THz spectroscopy, in fact, are largely determined not by individual sugar molecules but by their complexes that make up MHs.It would be interesting to carry out similar work on separating the contributions to hydration of individual unbound molecules  5).Data for water are taken from our previous work [39].
As follows from Figure 4a, the hydration of individual sugar molecules in solution is accompanied by much less strengthening of water binding than hydration of MHs.The increase in the number of free water molecules due to the hydration of individual fructose molecules is less than due to the hydration of MHs (Figure 4b).At the same time, the hydration of individual fructose molecules is accompanied by a greater increase in the number of hydrogen bonds than with MHs hydration (Figure 4c).Thus, the previously obtained data in various papers on the characteristics of the hydration of sugar molecules based on THz spectroscopy, in fact, are largely determined not by individual sugar molecules but by their complexes that make up MHs.It would be interesting to carry out similar work on separating the contributions to hydration of individual unbound molecules and MHs of other types of molecules-for example, proteins.Protein hydration in solutions has been actively studied using THz spectroscopy [29,70,71].Since there is evidence of the presence of MHs in amino acid solutions [10], the formation of MHs in protein solutions is not excluded.

Conclusions
In this paper, the THz-TDS method was used to study MHs, representing stable formations with an increased concentration of the dissolved substance formed in most solutions, using the example of glucose, fructose, and sucrose solutions.Based on the parameters of sugar hydration calculated from THz dielectric spectra of solutions, it was shown that the water binding in MHs of all three sugar solutions is increased compared to water in molecular solutions when MHs are destroyed by filtration.This effect for fructose solution is more pronounced than for others.Also, the MHs of fructose solution are characterized by a decrease in the number of hydrogen bonds between water molecules and an increase in the number of free water molecules.That is, fractionation of hydrate water molecules in fructose MHs is observed: in some areas, they are more strongly bound; in others, they are more weakly bound.These features of hydration within MHs of fructose, which are not manifested in MHs of glucose and sucrose, are apparently associated with constantly occurring mutarotations of fructose molecules, leading to significant rearrangements of hydrated water in MHs.This work clearly demonstrates that the THz-TDS method is able to provide new information about the structure of poorly studied MHs in solutions at the level of their hydration characteristics.It is also shown that the presence of MHs in solutions is an essential factor that must be taken into account when studying the hydration of various molecules in solutions by THz spectroscopy.

Figure 2 .
Figure 2. Transmission and refractive index spectra of solutions of 0.5 mol% glucose-(a,d), fructose-(b,e), and sucrose-(c,f) containing MHs, and molecular solutions of the same composition after filtration.

Figure 1 .
Figure 1.Size distributions of optical inhomogeneities registered in solutions of 0.5 mol% glucose, fructose, and sucrose by dynamic light scattering.Solutions before filtration (a); after filtration (b).

Figure 1 .
Figure 1.Size distributions of optical inhomogeneities registered in solutions of 0.5 mol% glucose, fructose, and sucrose by dynamic light scattering.Solutions before filtration (a); after filtration (b).

Figure 2 .
Figure 2. Transmission and refractive index spectra of solutions of 0.5 mol% glucose-(a,d), fructose-(b,e), and sucrose-(c,f) containing MHs, and molecular solutions of the same composition after filtration.

Figure 2 .
Figure 2. Transmission and refractive index spectra of solutions of 0.5 mol% glucose-(a,d), fructose-(b,e), and sucrose-(c,f) containing MHs, and molecular solutions of the same composition after filtration.

Figure 3 .
Figure 3. Average DS of the aqueous phase of solutions of 0.5 mol% glucose-, fructose-, and sucrosecontaining MHs, and molecular solutions of the same composition after filtration (a-c).DS difference spectra: Subtracting the spectrum of a solution containing MHs from the spectrum of a molecular solution (d-f).

Figure 4 Figure 4 . 2 ⁄
Figure 4. Comparison of the studied solutions with water according to parameters Δε1 (a),   0 2 ⁄ (b) of the model (3) and percentage of free water molecules (c) calculated by the Equation (5).Data for water are taken from our previous work[39].

Figure 4 .
Figure 4. Comparison of the studied solutions with water according to parameters ∆ε 1 (a), A/ω 2 0 (b) of the model (3) and percentage of free water molecules (c) calculated by the Equation (5).Data for water are taken from our previous work[39].